In the contemporary information transmission art, information is routinely sent across a transmission medium as a digital signal--i.e., a signal for which both time and amplitude are discrete, whether that information is inherently represented in an analog or digital form. In the case of information which is originally in an analog form, the continuous analog signal is sampled at predetermined intervals to arrive at a sequence of discrete numbers--each being representative of a value of the continuous signal at that sample point. After such a "digitizing" procedure, there is no difference from the standpoint of the transmission infrastructure between such analog-originated information and information which originates in a digital form.
Signal processing of information signals transmitted over a channel occurs in a wide variety of applications and with many objectives. Typical reasons for signal processing include: estimation of characteristic signal parameters; elimination or reduction of unwanted interference; and transformation of a signal into a form that is in some manner more useful or informative. Such processing of discrete (or digital) information signals is carried out by Digital Signal Processing ("DSP") techniques. Applications of DSP techniques currently occur in such diverse fields as acoustics, sonar, radar, geophysics, communications and medicine.
Processing elements which operate on a digital signal frequently occur as filters or equalizers, which are typically represented in the form shown in FIG. 1. There, x.sub.n represents an input signal at a given clock interval, n, delay registers 10 hold values of the input signal for preceding clock intervals, multipliers 11 produce the product of the signal from taps along the input line and coefficients, C.sub.i (i=0, 1, . . . , n-1), and those products are added by adders 12 to form the output signal y.sub.n. As can be seen in the figure, a characteristic of such a tapped delay line is that an output is a function of an input signal (including, in some cases, prior values of that input signal) and coefficients corresponding to the taps. Algebraically, that relationship would generally be of the form: EQU Y.sub.n =C.sub.0 x.sub.n +C.sub.1 x.sub.n-1 +C.sub.2 x.sub.n-2 +. . . +C.sub.n-1 x.sub.1
where y represents an output signal, x represents an input signal and C.sub.0, C.sub.1, . . . C.sub.n-1 are representative of the coefficients.
A comparatively recent variation in digital signal processing is known as adaptive signal processing which has developed concurrently with rapid advances in processing power for DSP hardware devices. A significant difference between classical signal processing techniques and the methods of adaptive signal processing is that the latter are generally applied for time varying digital systems. For the adaptive signal processing case of adaptive filtering, a filter (or equalizer) is caused to adapt to changes in signal statistics so that the output is as close as possible to some desired signal. Adaptive filtering will often be applied for the recovery of an input signal after transmission of that signal over a noisy channel.
Various adaptation algorithms are well known in the art and need not be discussed herein. However, it should be observed that the general adaptation process for an adaptive filter or equalizer operates on the tap coefficients of such a filter or equalizer by iteratively adjusting such coefficients to progress toward the achievement of a desired objective--e.g. a signal to noise ratio above a defined threshold. The general adaptation process can be described algebraically as: EQU C'=C.+-.u
where C' is the value of coefficient C after an adaptation iteration and u represents an update term added by the adaptation iteration. It should be understood of course that each coefficient in a filter will be updated in this same manner and that the update term u may, and likely will, vary from coefficient to coefficient. In a conventional digital system those coefficient values will be expressed as binary numbers.
In practice, adaptive filters and equalizers typically have a large number of taps and a corresponding large number of coefficients. It is not at all uncommon for such an adaptive filter or equalizer to have on the order of 256 coefficients. A characterization of such adaptive filters/equalizers is that most of the coefficients at any given time are quite small.
To illustrate the reason for this phenomenon, consider an equalizer used to cancel "ghost" signals along a transmission line. Since the designer of the equalizer usually will have no information as to the actual location of such "ghost" signals on the transmission line, the equalizer is designed with taps (and coefficients) covering positions all along the transmission line. Although the equalizer coefficients of interest will appear at the points where actual "ghost" signals occur in the transmission line, and will be of comparatively large magnitude, a large number of small, non-zero coefficients will also be produced by the equalizer due to noise or other random conditions.
Since such small coefficients generally do not correspond to actual transmission line anomalies, the equalizing "correction" which they represent is actually a degradation in the output signal. Processing of such "false" coefficient signals also represents unwanted processor overhead and can, as well, reduce the useful life of processor components.